Liquidation cost calculation

ABSTRACT

A set of estimated allocations N est (X 1 ) through N est (X k ) of portfolio positions to products X 1  through X k  may be determined, with products X 1  through X k  including portfolio products and spread-traded products based on some of the portfolio products. Utilizing the set of estimated allocations, an optimized liquidation cost LC opt  may be designated. Data indicating at least a portion of a performance bond based on the optimized liquidation LC opt  may be output.

REFERENCE TO RELATED APPLICATIONS

This application is a continuation under 37 C.F.R. § 1.53(b) of U.S.patent application Ser. No. 15/442,194 filed Feb. 24, 2017 now U.S. Pat.No. 10,643,282, which is a continuation under 37 C.F.R. § 1.53(b) ofU.S. patent application Ser. No. 14/450,632, filed Aug. 4, 2014, theentire disclosures of all of the above applications are herebyincorporated by reference and relied upon.

BACKGROUND

In many financial markets, holders of positions in traded assets arerequired to maintain a minimum balance of cash or other assets as aperformance bond. This performance bond may be used to reduce the riskto other market participants of losses associated with the positionholder failing to fulfill its obligations. If a holder of a portfoliogoes bankrupt or otherwise defaults, the performance bond for thatportfolio can be used to reduce losses resulting from the holder nolonger being able to cover its positions. It is desirable to a baseperformance bond requirement for a portfolio on an accurate estimate ofamounts that might be recoverable when liquidating that portfolio.However, attempting to liquidate a large position in a particularfinancial product can itself significantly affect the market for thatproduct. As a result, estimating liquidation recovery becomes moredifficult as position sizes increase. There remains a need for improvedsystems and techniques to calculate a performance bond value that betteraccounts for liquidation costs.

SUMMARY

This Summary is provided to introduce a selection of concepts in asimplified form that are further described below in the DetailedDescription. This Summary is not intended to identify key features oressential features of the invention.

In some embodiments, portfolio data may be accessed. That portfolio datamay define, for each of a plurality of outright-traded products, aportfolio position in the outright-traded product. Data defining aliquidation set of products X₁ through X_(k) may be identified. Theproducts X₁ through X_(k) may include the plurality of outright-tradedproducts and further include one or more spread-traded products, each ofthe spread-traded products may represent a combination of two or more ofthe outright-traded products, and each of the products X₁ through X_(k)may respectively correspond to one of cost functions C₁ through C_(k)for estimating a liquidation cost based on notional value. A set ofestimated allocations N_(est)(X₁) through N_(est)(X_(k)) of theportfolio positions to products X₁ through X_(k) may be identified.Calculations may be performed, utilizing the estimated allocationsN_(est)(X₁) through N_(est)(X_(k)), to determine a set of allocationsN(X₁) through N(X_(k)) corresponding to a liquidation cost LC that isless than a liquidation cost LC_(est) corresponding to the set ofestimated allocations. An optimized liquidation cost LC_(opt) may bedesignated. Data indicating at least a portion of a performance bondbased on the optimized liquidation LC_(opt) may be output.

Embodiments include, without limitation, herein-described methods forprocessing data associated with liquidation costs and/or performancebonds, computer systems configured to perform such methods, andnon-transitory computer-readable media storing instructions executableby a computer system to perform such methods.

BRIEF DESCRIPTION OF THE DRAWINGS

Some embodiments are illustrated by way of example, and not by way oflimitation, in the figures of the accompanying drawings and in whichlike reference numerals refer to similar elements.

FIG. 1 shows an exemplary trading network environment for implementingtrading systems and methods according to at least some embodiments.

FIG. 2 is a flow chart of a method according to some embodiments.

FIGS. 3 and 4 show states of a computer system module after performingcertain steps of the method of FIG. 2.

FIG. 5 shows operations performed by a computer system module in someembodiments when estimating an allocation of portfolio positions toproducts in a liquidation set.

FIG. 6 is a flow chart showing operations performed by a computer systemmodule in some embodiments when estimating an allocation of portfoliopositions to products in a liquidation set.

FIG. 7 shows operations performed by a computer system module in someadditional embodiments when estimating an allocation of portfoliopositions to products in a liquidation set.

FIG. 8 is a flow chart showing operations performed by a computer systemmodule in some additional embodiments when estimating an allocation ofportfolio positions to products in a liquidation set.

FIG. 9 is a flow chart of a method according to some furtherembodiments.

DETAILED DESCRIPTION

In the following description of various embodiments, reference is madeto the accompanying drawings, which form a part hereof, and in whichvarious embodiments are shown by way of illustration. It is to beunderstood that there are other embodiments and that structural andfunctional modifications may be made. Embodiments of the presentinvention may take physical form in certain parts and steps, examples ofwhich will be described in detail in the following description andillustrated in the accompanying drawings that form a part hereof.

Various embodiments may comprise a method, a computer system, and/or acomputer program product. Accordingly, one or more aspects of one ormore of such embodiments may take the form of an entirely hardwareembodiment, an entirely software embodiment, and/or an embodimentcombining software and hardware aspects. Furthermore, such aspects maytake the form of a computer program product stored by one or morenon-transitory computer-readable storage media having computer-readableprogram code, or instructions, embodied in or on the storage media. Theterm “computer-readable medium” or “computer-readable storage medium” asused herein includes not only a single medium or single type of medium,but also a combination of one or more media and/or types of media. Sucha non-transitory computer-readable medium may store computer-readableinstructions (e.g., software) and/or computer-readable data (i.e.,information that may or may not be executable). Any suitable computerreadable media may be utilized, including various types ofnon-transitory computer readable storage media such as hard disks,CD-ROMs, optical storage devices, magnetic storage devices, FLASHmemory, and/or any combination thereof. The term “computer-readablemedium” or “computer-readable storage medium” could also include anintegrated circuit or other device having hard-coded instructions (e.g.,logic gates) that configure the device to perform one or moreoperations.

Aspects of method steps described in connection with one or moreembodiments may be executed by one or more processors associated with acomputer system (such as exchange computer system 100 described below).As used herein, a “computer system” could be a single computer or couldcomprise multiple computers. When a computer system comprising multiplecomputers performs a method, various steps could be performed bydifferent ones of those multiple computers. Processors of a computersystem may execute computer-executable instructions stored onnon-transitory computer-readable media. Embodiments may also bepracticed in a computer system forming a distributed computingenvironment, with tasks performed by remote processing devices that arelinked through a communications network. In a distributed computingenvironment, program modules may be located in both local and remotecomputer storage media including memory storage devices.

Exemplary Operating Environment

Aspects of at least some embodiments can be implemented with computersystems and computer networks that allow users to communicate tradinginformation. An exemplary trading network environment for implementingsystems and methods according to at least some embodiments is shown inFIG. 1. The implemented systems and methods can include systems andmethods, such as are described herein, that facilitate data processingand other activities associated with determination of liquidation costsand performance bonds based at least in part on such liquidation costs.

Computer system 100 can be operated by a financial product exchange andconfigured to perform operations of the exchange for, e.g., trading andotherwise processing data relating to various financial products.Financial products of the exchange may include, without limitation,futures contracts, options on futures contracts, other types of options,and other types of derivative contracts. Financial products traded orotherwise processed by the exchange may also include over-the-counter(OTC) products such as OTC forwards, OTC options, OTC swaps, etc.Financial products traded through the exchange may also or alternativelyinclude other types of financial interests, including without limitationstocks, bonds and/or other securities (e.g., exchange traded funds),foreign currencies, and spot market trading of commodities. In at leastsome embodiments, and as explained in more detail below, financialproducts traded and/or otherwise processed through exchange computersystem 100 include financial products in a portfolio for which aliquidation cost and performance bond are being calculated.

Computer system 100 receives orders for financial products, matchesorders to execute trades, transmits market data related to orders andtrades to users, and performs other operations associated with afinancial product exchange. Exchange computer system 100 may beimplemented with one or more mainframe, desktop or other computers. Inone embodiment, a computer device uses a 64-bit processor. A userdatabase 102 includes information identifying traders and other users ofexchange computer system 100. Data may include user names and passwords.An account data module 104 may process account information that may beused during trades. A match engine module 106 is included to matchprices and other parameters of bid and offer orders. Match engine module106 may be implemented with software that executes one or morealgorithms for matching bids and offers.

A trade database 108 may be included to store information identifyingtrades and descriptions of trades. In particular, a trade database maystore information identifying the time that a trade took place and thecontract price. An order book module 110 may be included to store pricesand other data for bid and offer orders, and/or to compute (or otherwisedetermine) current bid and offer prices. A market data module 112 may beincluded to collect market data, e.g., data regarding current bids andoffers for futures contracts, futures contract options, and otherderivative products. Module 112 may also prepare the collected marketdata for transmission to users. A risk management module 134 may beincluded to compute and determine a user's risk utilization in relationto the user's defined risk thresholds. An order processor module 136 maybe included to decompose delta based and bulk order types for furtherprocessing by order book module 110 and match engine module 106.

A clearinghouse module 140 may be included as part of exchange computersystem 100 and configured to carry out operations of a clearinghouse ofthe exchange that operates computer system 100. Module 140 may receivedata from and/or transmit data to trade database 108 and/or othermodules of computer system 100, including liquidation cost determinationmodule 142, regarding trades of futures contracts, futures contractsoptions, and other financial products traded through the exchange thatoperates system 100. Clearinghouse module 140 may facilitate thefinancial product exchange (or a clearinghouse of the exchange) actingas one of the parties to every traded contract or other product. Forexample, computer system 100 may match an offer by party A to sell afutures contract, an option or another exchange-traded financial productwith a bid by party B to purchase a like exchange-traded financialproduct. Module 140 may then create an exchange-traded financial productbetween party A and the exchange clearinghouse and a secondexchange-traded financial product between the exchange clearinghouse andparty B. Module 140 may similarly create offsetting contracts whencreating contracts as a result of an option exercise and/or may selectoption grantors to fulfill obligations of exercising option holders.Module 140 may also be configured to perform other clearinghouseoperations. As a further example, module 140 may maintain performancebond data with regard to clearing members and/or trading customers. Aspart of such operations, module 140 may store and maintain dataregarding the values of various options, futures contracts, and otherinterests, determine mark-to-market and final settlement amounts,confirm receipt and/or payment of amounts associated with performancebond accounts, confirm satisfaction of delivery and other finalsettlement obligations, etc.

Clearinghouse module 140 may include a liquidation cost determinationmodule 142. Module 142 may generate, store, and process data associatedwith liquidation costs for portfolios. Various operations performed bymodule 142 in at least some embodiments are further described below.

Each of modules 102 through 142 could be implemented as separatesoftware components executing within a single computer, separatehardware components (e.g., dedicated hardware devices) in a singlecomputer, separate computers in a networked computer system, or anycombination thereof (e.g., different computers in a networked system mayexecute software modules corresponding more than one of modules102-142). When one or more of modules 102 through 142 are implemented asseparate computers in a networked environment, those computers may bepart of a local area network, a wide area network, and/or multipleinterconnected local and/or wide area networks.

Exchange computer system 100 may also communicate in a variety of wayswith devices that may be logically distinct from computer system 100.For example, computer device 114 is shown directly connected to exchangecomputer system 100. Exchange computer system 100 and computer device114 may be connected via a T1 line, a common local area network (LAN),or other mechanism for connecting computer devices. Computer device 114is shown connected to a radio 132. The user of radio 132 may be a traderor exchange employee. The radio user may transmit orders or otherinformation to a user of computer device 114. The user of computerdevice 114 may then transmit the trade or other information to exchangecomputer system 100.

Computer devices 116 and 118 are coupled to a LAN 124 and maycommunicate with exchange computer system 100 via LAN 124. LAN 124 mayimplement one or more of the well-known LAN topologies and may use avariety of different protocols, such as Ethernet. Computers 116 and 118may communicate with each other and other computers and devicesconnected to LAN 124. Computers and other devices may be connected toLAN 124 via twisted pair wires, coaxial cable, fiber optics, radiolinks, or other media.

A wireless personal digital assistant device (PDA) 122 may communicatewith LAN 124 or the Internet 126 via radio waves. PDA 122 may alsocommunicate with exchange computer system 100 via a conventionalwireless hub 128. As used herein, a PDA includes mobile telephones andother wireless devices that communicate with a network via radio waves.

FIG. 1 also shows LAN 124 connected to the Internet 126. LAN 124 mayinclude a router to connect LAN 124 to the Internet 126. Computer device120 is shown connected directly to the Internet 126. The connection maybe via a modem, DSL line, satellite dish, or any other device forconnecting a computer device to the Internet. Computers 116, 118, and120 may communicate with each other via the Internet 126 and/or LAN 124.

One or more market makers 130 may maintain a market by providingconstant bid and offer prices for a derivative or security to exchangecomputer system 100. Exchange computer system 100 may also include tradeengine 138. Trade engine 138 may, e.g., receive incoming communicationsfrom various channel partners and route those communications to one ormore other modules of exchange computer system 100.

One skilled in the art will appreciate that numerous additionalcomputers and systems may be coupled to exchange computer system 100.Such computers and systems may include, without limitation, additionalclearing systems, regulatory systems, and fee systems.

The operations of computer devices and systems shown in FIG. 1 anddescribed herein may be controlled by computer-executable instructionsstored on one or more non-transitory computer-readable media. Forexample, computer device 116 may include computer-executableinstructions for receiving market data from exchange computer system 100and displaying that information to a user. As another example, module140 and/or module 142 and/or other modules of exchange computer system100 may include one or more non-transitory computer-readable mediastoring computer-executable instructions for performing herein-describedoperations associated with liquidation cost data and/or performance bonddata.

Of course, numerous additional servers, computers, handheld devices,personal digital assistants, telephones, and other devices may also beconnected to exchange computer system 100. Moreover, one skilled in theart will appreciate that the topology shown in FIG. 1 is merely anexample and that the components shown in FIG. 1 may be connected bynumerous alternative topologies.

Exemplary Embodiments

In at least some embodiments, exchange computer system 100 (or “computersystem 100”) receives, stores, generates, and/or otherwise processesliquidation cost and performance bond data, as described herein, for oneor more portfolios. In the following description of some embodiments,some or all of these operations may be performed by clearinghouse module140 (including liquidation cost module 142) of computer system 100. Inother embodiments, however, some or all of these operations may beperformed by other modules of computer system 100 and/or by modules ofone or more other computer systems. In some embodiments, for example,clearinghouse operations may be performed by one or more computersystems separate from an exchange computer system, with one or more ofthe operations described herein performed by those one or more separatecomputer systems.

As used herein, “portfolio” refers to a collection of positions that theportfolio holder possesses with regard to one or more products. Productsmay include, without limitation, OTC foreign currency (FX) forwards,other types of OTC forwards, OTC swaps, futures, options and otherproducts described above. As used herein, “product” refers to a categoryof contracts or other type of arrangement that have similar terms. Forexample, product Y₁ might be a type of OTC forward contract requiringdelivery of 1,000,000 US dollars on future date D₁ in return for anegotiated contractual price designated in Euros. Product Y₂ might alsobe a type of OTC forward contract requiring delivery of 1,000,000 USdollars in return for a negotiated contractual price designated inEuros, but having a different delivery date D₂. A product isdistinguished from individual instances of that product. For example, aninstance of product Y₁ would be a single OTC forward contract.

“Position” refers to the amount by which a particular product may berepresented in a portfolio. Typically, a position in a particularproduct is quantified based on some multiple of a notional value forthat product. For example, product Y₁ might be treated as having anotional value of $1,000,000US. A portfolio that includes identicalinterests in five such contracts would thus have a position of$5,000,000US in product Y₁. Notional values may be defined in other waysfor other types of products. A notional need not be a quantity of acurrency.

A position in a product is further characterized by a side of thetransaction corresponding to the product in question. In an OTC forwardcontract or in a futures contract, for example, a “long” positioncorresponds to the side of the transaction obligated to pay the contractprice and receive the underlying contract subject matter (or“underlying”) at a contractually-designated time. A “short” positioncorresponds to the side of the transaction obligated to deliver theunderlying and receive the contract price at thecontractually-designated time. Continuing the previous example, if theportfolio holder has long interests in the five product Y₁ contracts,and if each of those five contracts has the same contract price of734,000 Euros, the portfolio holder would be obligated to pay 3,670,000(5×734,000) Euros on date D₁ and to receive a total of $5,000,000US. Ifthe portfolio holder has short interests in the five Y₁, the portfolioholder would be obligated to deliver a total of $5,000,000US on date D₁and to receive 3,670,000 Euros.

Notional value is distinct from market value. Continuing a previousexample, a portfolio holder may enter into a Y₁ contract at price P. Ona subsequent date D, with D being after execution of the Y₁ contract butprior to D₁, market forces may have caused the exchange rate for Eurosand dollars to change. If the portfolio holder wishes to close out thatcontract (e.g., by obtaining an offsetting interest in another Y₁contract), the contract price of that offsetting contract may differfrom P by an amount ΔP (which may be positive or negative).

Products may include products that are traded outright, as well asproducts traded as a spread. A spread-traded product, in effect,represents a combination of outright-traded products. Continuing anearlier example, product Y₁ is traded outright, i.e., is“outright-traded.” A party wishing to have a Y₁ position may enter intoone or more instances of product Y₁ by negotiating for entry into Y₁contracts only. Product Y₂ is similarly outright-traded. Products Y₁ andY₂ may also form components (or “leg products”) of another product Y₃that is spread-traded. For example, product Y₃ may be defined as a typeof combination that includes a long position in a Y₁ contract and ashort position in a Y₂ contract (LY₁-SY₂) or a short position in a Y₁contract and a long position in a Y₂ contract (SY₁-LY₂). A spread-tradedproduct may have more than two leg products. A position in aspread-traded product may also be characterized as long or short.Because a spread-traded product includes a combination of long and shortpositions in the leg products, however, the definition of the long andshort position may vary.

A spread-traded product may be traded as a combination of its legproducts. After executing such a trade, however, there are separateportfolio positions in each of the leg products. For example,spread-traded products may be traded by quoting a price that representsa difference between the prices of the individual leg products. A partywishing to acquire a position in a Y₃ product might agree to do so at aprice P_(spr) representing a difference between the price of a longinterest in a Y₁ contract and a short interest in a Y₂ contract. Oncethat trade is executed, the portfolio of that party then includes a longposition in product Y₁ and a short position in product Y₂.

When liquidating a large portfolio (e.g., upon default a largeinstitutional investor), it may be necessary to either buy out oracquire offsetting positions for all positions in the portfolio.However, a sudden purchase or sale of a large interest in a particularproduct can significantly affect the market and cause prices for thatproduct to be higher or lower than they might otherwise be. This effecton price, also known as liquidation cost, can be considered a portion ofa large portfolio position value that may be lost because of a need toliquidate that position in a market that is abnormally depressed orinflated because of the sudden availability of that large position inthe market. Liquidation cost for a particular product can beapproximated as a function C(N( )), where “N( )” represents the totalnotional value of a position in that product. A liquidation costfunction can normally be generated by polling brokers and/or othermarket participants and obtaining sample prices for different sizedpositions in a particular product. The resulting data can then beconverted into a function using conventional curve fitting techniques.For example, a cost function for a product X may take the form shown inEquation 1.

$\begin{matrix}{{C\left( {N(X)} \right)} = {a*\left( {b + {d*e^{\frac{- {({N{(X)}})}^{2}}{d}}}} \right)}} & {{Equation}\mspace{14mu} 1}\end{matrix}$

In Equation 1, “e” is Euler's constant and a, b and d are constantsdetermined by curve fitting to the sample data. Because liquidation costnormally increases for increasing notional value, a, b and d typicallyhave values such that a*b is positive and a*d is negative.

For a portfolio having positions in k products, the liquidation cost isthe sum of the liquidation costs of each component. This can berepresented as shown by Equation 2.

$\begin{matrix}{{LC}{= {\sum\limits_{i = 1}^{k}{C_{i}\left( {N\left( X_{i} \right)} \right)}}}} & {{Equation}\mspace{14mu} 2}\end{matrix}$

In Equation 2, “LC” is the liquidation cost for the portfolio,“N(X_(i))” is the total notional of the portfolio position in the i^(th)product, and “C_(i)( )” is the liquidation cost function for the i^(th)product.

Determining an accurate liquidation cost for a portfolio is more complexthan is suggested by Equation 2, however. In practice, a liquidationcost for a spread-traded product is less than the liquidation costs ofthe outright trading of the leg products. To illustrate using a previousexamples, assume that a portfolio includes a $500 million long positionin product Y₁ ($500M LY₁) and a $500 million short position in productY₂ ($500M SY₂). This is equivalent to a $500 million position in a Y₃product having Y₁ and Y₂ leg products. The cost of liquidating the Y₁and Y₂ positions as outright-traded products may be significantly morethan liquidating those positions as an LY₁-SY₂ Y₃ spread. Stateddifferently, and if C_(Y1), C_(Y2) and C_(Y3) are the liquidation costfunctions for products Y₁, Y₂ and Y₃, respectively, thenC_(Y3)($500M)<C_(Y1)($500M)+C_(Y2)($500M). Moreover, there may bemultiple spread-traded products into which a particular group ofportfolio positions could be allocated. Each of those multiplespread-traded products may have a different cost function, so differentallocations can result in significantly different total liquidationcosts.

FIG. 2 is a flow chart of a method according to some embodiments Themethod of FIG. 2 predicts a total liquidation cost for a portfolio andthen generates and outputs data indicating a performance bond (or aperformance bond component) based on that predicted liquidation cost.Operations corresponding to the steps in FIG. 2 may be carried out bymodules 140 and 142 of computer system 100 or by another computersystem.

In step 201, computer system 100 accesses data associated with a subjectportfolio for which a performance bond amount is being determined. Insome embodiments the accessed data may include, for each of multipleproducts represented in a portfolio (“portfolio products”), a totalnotional value of the portfolio position in that product and anindication of whether that position is short or long. As but oneexample, the accessed data for a portfolio of j products X₁ throughX_(j) could take the form of an array similar to Data Array 1.

${Data}\mspace{14mu}{Array}\mspace{14mu} 1\text{:}\mspace{14mu}\begin{Bmatrix}X_{1} & {N_{P}\left( X_{1} \right)} & \lbrack{side}\rbrack \\\vdots & \vdots & \vdots \\X_{j} & {N_{P}\left( X_{j} \right)} & \lbrack{side}\rbrack\end{Bmatrix}$

In Data Array 1, each row corresponds to a different one of theportfolio products. The first element in each row is an identifier ofthe portfolio product to which the row corresponds. The second elementin the row is the total notional value of the portfolio position in thatproduct (e.g., N_(P)(X₁) is the total notional value of the portfolioposition in product X₁). The third element in each row is an indicatorof what side the position may be (i.e., long or short). An example ofStep 201 is further discussed in connection with FIG. 3.

In step 202, computer system 100 identifies data that defines aliquidation set of products. The liquidation set may include theportfolio products, but may additionally include spread-traded productsthat represent combinations of the portfolio products, i.e., productsthat include some of the portfolio products as leg products. As but oneexample, the identified data could take the form of an array similar toData Array 2.

${Data}\mspace{14mu}{Array}\mspace{14mu} 2\text{:}\mspace{14mu}\begin{Bmatrix}X_{1} & \lbrack{outright}\rbrack \\\vdots & \vdots \\X_{j} & \lbrack{outright}\rbrack \\X_{j + 1} & \left\lbrack {{leg}\mspace{11mu}{products}} \right\rbrack \\\vdots & \vdots \\X_{k} & \left\lbrack {{leg}\mspace{14mu}{products}} \right\rbrack\end{Bmatrix}$

The data in rows 1 through j of Data Array 2 correspond to the sameportfolio products represented in Data Array 1. Each of rows 1 through jincludes an identifier of for one of the portfolio products and dataindicating that the product is outright-traded. Each of the subsequentrows j+1 through k of Data Array 2 corresponds to a different one ofspread-traded products X_(j+1) through X_(k). Each of thosespread-traded products includes two or more of the portfolio products asleg products. Each of rows j+1 through k includes an identifier of thecorresponding spread-traded product and data indicating the legproducts. If, for example, product X_(j+1) is a type of spreadcomprising a position in an X₁ product and an opposite position in an X₂product, the “leg products” description data might indicate “LX₁-SX₂ orSX₁-LX₂,” or simply “X₁-X₂” if it is understood that all of thespread-traded products involve opposite interests in adjacent legs.

As part of step 202, computer system 100 may identify data that definesliquidation cost functions for each of the products in the liquidationset. As but one example, the identified data could take the form of anarray similar to Data Array 3.

${Data}\mspace{14mu}{Array}\mspace{14mu} 3\text{:}\mspace{14mu}\begin{Bmatrix}C_{1} \\\vdots \\C_{j} \\C_{j + 1} \\\vdots \\C_{k}\end{Bmatrix}$

Each element in Data Array 3 represents a liquidation cost function forone of the products in the liquidation set of Data Array 3, e.g., “C₁”is the liquidation cost function for product X₁. Although the example ofData Arrays 1, 2 and 3 suggests at least three portfolio products and atleast three spread-traded products, this need not be the case. Anexample of step 202 is further discussed in connection with FIG. 4.

In step 203, computer system 100 determines a set of estimatedallocations of the portfolio positions among the products of theliquidation set. This set of estimated allocations is subsequently usedas an approximation to help narrow a search for an optimized allocationin step 204. In some embodiments, and as described below in connectionwith FIGS. 5 and 6, the estimation of step 203 may comprise ordering thespread-traded products in the liquidation set based on the costfunctions corresponding to the spread-traded products, progressingthrough each of the ordered spread-traded products and allocating theportfolio positions to hypothetical trades in the spread-traded productsto the maximum extent possible, and allocating any remainder of theportfolio positions to hypothetical outright trades. In otherembodiments, and as described below in connection with FIGS. 7 and 8,the estimation of step 203 may comprise generating multiple searchtrees, with each of the search trees having multiple branches,determining a set of allocations and a liquidation cost corresponding toeach of at least a portion of the branches in each of the search trees,and selecting the set of allocation corresponding to the lowestliquidation cost.

In step 204, and as discussed in further detail below, computer system100 performs calculations to determine a set of optimized allocations ofthe subject portfolio positions among the liquidation set products. Theset of estimated allocations from step 203 may be used in step 204. Instep 205, computer system 100 determines whether it was able to find aset of allocations having a liquidation cost LC that is less than theliquidation cost LC_(est) corresponding to the set of estimatedallocations from step 203. If not, LC_(est) is designated as LC_(opt) instep 206 and computer system 100 proceeds to step 208. If a set ofallocations was found, the liquidation cost LC is designated as LC_(opt)and computer system 100 proceeds to step 208. In step 208, computersystem 100 calculates a performance bond amount (or an amount of aperformance bond component) and outputs data indicative of thatperformance bond amount (or component). Based on that output data, adetermination might be made with regard to whether the holder of thesubject portfolio has sufficient funds or other assets on account tocover potential losses. If necessary, additional funds can be collected.

In some embodiments, step 208 may comprise calculating a firstperformance bond component based on the optimized liquidation cost and asecond performance bond component calculated in another manner (e.g.,based on market value of the portfolio without consideration ofliquidation cost). In some such embodiments, the liquidation costcomponent may be a predetermined percentage of the liquidation cost andthe market value component may be a predetermined percentage of theportfolio market value exclusive of liquidation cost.

To further assist in describing operations according to certainembodiments, Table 1 provides a hypothetical portfolio P1 for use insubsequent examples.

TABLE 1 Hypothetical Portfolio P1 total notional position product(×$1,000,000 US) side X₁ 1200 Long X₂ 800 Short X₃ 500 Short X₄ 750 LongX₅ 600 Short X₆ 1000 Long

As seen in Table 1, portfolio P1 includes positions in products X₁through X₆. Each of products X₁ through X₆ is an outright-traded productsuch as an OTC FX forward contract. For simplicity, it is assumed thateach of these products has a defined notional value of $1,000,000US,i.e., that the notional value of a single product instance is$1,000,000. Thus, for example, the $1.2 billion long position in productX₁ represents long positions in 1200 instances of the X₁ product, the$800 million short position in product X₂ represents short positions in800 instances of the X₂ product, etc. Products represented in aportfolio may have different defined notionals. Normally, however, aportfolio position in a particular product will be an integer multipleof the defined notional of that product.

FIG. 3 shows module 142 of computer system 100 at the completion of step201 of FIG. 2, where module 142 has accessed data 301 that defines thepositions of portfolio P1. In particular, data 301 identifies theproducts represented in portfolio P1, sizes of the positions in theproducts, and the nature of each position (long or short). FIG. 4 showsmodule 142 at the completion of step 202 of FIG. 2, where module 142 hasidentified data 302 that defines a liquidation set. In the presentexample, the liquidation set includes outright-traded portfolio productsX₁-X₆, as well as six spread-traded products X₇-X₁₂. Each ofspread-traded products X₇-X₁₂ includes two of portfolio products X₁-X₆as its leg products, as shown in Table 2 and in FIG. 4.

TABLE 2 product leg products X₇ X₁-X₂ (LX₁-SX₂ or SX₁-LX₂) X₈ X₁-X₃(LX₁-SX₃ or SX₁-LX₃) X₉ X₂-X₃ (LX₂-SX₃ or SX₂-LX₃) X₁₀ X₂-X₄ (LX₂-SX₄ orSX₂-LX₄) X₁₁ X₃-X₅ (LX₃-SX₅ or SX₃-LX₅) X₁₂ X₃-X₆ (LX₃-SX₆ or SX₃-LX₆)

As further shown in FIG. 4, module 142 has also accessed data 303 thatdefines liquidation cost functions C₁ through C₁₂ that respectivelycorrespond to products X₁ through X₁₂ in the liquidation set.

FIG. 5 shows operations performed by module 142 in some embodiments, aspart of step 203 of FIG. 2 and with regard to portfolio P1, whenestimating an allocation of portfolio P1 positions to the products inthe liquidation set. Although not shown in FIG. 5, module 142 orderseach of spread-traded products X₇ through X₁₂ based on theircorresponding liquidation cost functions C₇ through C₁₂, resulting in aranking of products X₇ through X₁₂ from lowest corresponding liquidationcost function unit value to highest corresponding liquidation costfunction unit value. In some embodiments, a unit value for aspread-traded product liquidation cost function may be the value of thatfunction corresponding to the notional value of a single instance of aleg product. For example, products X₇-X₁₂ could be ordered bycalculating values for C₇($1,000,000), C₈($1,000,000), C₉($1,000,000),C₁₀($1,000,000), C₁₁($ 1,000,000), and C₁₂($1,000,000), ordering thefunctions from lowest to highest resulting values, and then orderingproducts X₇-X₁₂ based on the ordering of the functions. For simplicity,the example of FIG. 5 assumes that the ordering of products X₇ throughX₁₂ based on the unit size their corresponding liquidation costfunctions is the same as the numerical order of the subscriptsidentifying those products (e.g.,C₇(1000000)<C₈(1000000)<C₉(1000000)<C₁₀(1000000)<C₁₁(1000000)<C₁₂(1000000)).

After ordering the spread-traded products, and as shown at step a,module 142 attempts to allocate portfolio P1 positions to product X₇, tothe maximum extent possible, without increasing any portfolio positions.As part of step a, module 142 first determines if any allocation toproduct X₇ is possible by evaluating whether the portfolio has remaining(not yet allocated) oppositely-sided positions in the X₇ leg products.In this example, portfolio P1 has a remaining $1200 million long X₁position and a remaining $800 million short X₂ position, so allocationto a hypothetical X₇ product trade can proceed. Because an X₇ productinstance includes equal-sized positions in the leg products, the smallerof the remaining X₁ and X₂ positions is chosen as the size of theallocation. If the larger of the remaining X₁ and X₂ positions werechosen as the size of the allocation to product X₇, it would benecessary to first (hypothetically) increase the portfolio shortposition in product X₂ to $1,200,000.

At the conclusion of step a, all of the X₂ position and $800 million ofthe X₁ position have been allocated to a hypothetical trade in productX₇. This is represented in FIG. 5 as N_(est)(X₇)=800. As shown at stepb, the remaining portfolio positions are updated to reflect thisallocation. A similar sequence occurs at step c, resulting in allocatingthe remaining X₁ position and $400 million of the X₃ position to ahypothetical trade in product X₈ (N_(est)(X₈)=400), and at step d,resulting in further updating of the remaining portfolio P1 positions.At step e, a zero allocation to product X₉ occurs (N_(est)(X₉)=0), asthere is no remaining portfolio position to allocate to the X₂ leg ofX₉. At step f, a zero allocation to product X₁₀ occurs (N_(est)(X₁₀)=0),as there is no remaining portfolio position to allocate to the X₂ leg ofX₁₀. At step g, a zero allocation to product X₁₁ occurs(N_(est)(X₁₁)=0), as there are not opposite remaining portfoliopositions in the X₃ and X₅ legs of X₁₁. At step h, the remaining $100million short X₃ position and $100 million of the remaining $1,000million long X₆ position are allocated to a hypothetical trade inproduct X₁₂ (N_(est)(X₁₂)=100). The remaining positions are updated(step i) and then allocated to hypothetical outright trades in thecorresponding products (step j). After step j, and as shown in FIG. 5,estimated allocations of all portfolio P1 positions have been made toproducts in the liquidation set. This allocation is estimated because,as described below, it is may not be the final allocation and may onlybe used to assist calculation of an optimized allocation. The estimatedliquidation cost LC_(est) associated with a set of estimated allocationsN_(est)(X₁) through N_(est)(X_(k)) can be calculated using Equation 3.

$\begin{matrix}{{LC_{est}} = {\sum\limits_{i = 1}^{k}{C_{i}\left( {N_{est}\left( X_{i} \right)} \right)}}} & {{Equation}\mspace{14mu} 3}\end{matrix}$

FIG. 6 is a flow chart summarizing operations performed by module 142 ofcomputer system 100 in embodiments such as the example described in FIG.5. The steps of FIG. 6 may form step 203 of FIG. 2. In step 321, thespread trade products in the liquidation set are sorted based on lowestcorresponding liquidation cost function unit value to highestcorresponding liquidation cost function unit value, and are ranked fromr=1 (lowest) to r=R (highest). In step 322, a counter for r isinitialized to 1. In step 323, module 142 begins consideration ofspread-traded product r. In step 324, module 142 determines ifallocation to spread-traded product r is possible (i.e., if there areremaining appropriately-sided portfolio positions in the leg products ofproduct r). If not, module 142 proceeds to step 326, described below. Ifallocation is possible, module 142 proceeds to step 325 and allocatesremaining portfolio positions to a hypothetical trade in spread-tradedproduct r to the maximum extent possible without increasing anyportfolio positions. That maximum allocation will be the smallestremaining portfolio interest in one of the r product leg products. Aspart of step 325, values of remaining portfolio interests are updated.In step 326, module 142 determines if r=R. If not, module 142 incrementsthe r counter by 1 at step 327 and returns to step 323. If r=R at step326, module 142 proceeds to step 328 and allocates any remainingportfolio positions to hypothetical trades in appropriateoutright-traded products.

FIG. 7 shows operations performed by module 142, in some alternateembodiments, instead of the operations described in connection withFIGS. 5 and 6. Although not shown in FIG. 7, module 142 first generatesmultiple orderings of the portfolio products X₁ through X₆. Three suchorderings are shown in FIG. 7: a first ordering X₁, X₂, X₃, X₄, X₅, X₆,a second ordering X₂, X₃, X₄, X₅, X₆, X₁, and a third ordering X₂, X₁,X₃, X₄, X₅, X₆. However, additional orderings may be included. In someembodiments, module 142 might generate all possible orderings ofproducts X₁ through X₆. Because this might ultimately result inextensive computations for portfolios with positions in numerousproducts, however, procedures may be implemented to limit the number oforderings generated. Examples of such procedures are provided below.

For each generated ordering of portfolio products, module 142 generatesa search tree. The following discussion of FIG. 7 only discusses thesearch tree associated with the first ordering (X₁, X₂, X₃, X₄, X₅, X₆).For convenience, this tree is referred to as the “first tree.” Thesearch trees associated with the second ordering, the third ordering andany other orderings can be generated in a manner similar to thatdescribed in connection with the first tree.

The first level nodes of the first tree include all spread-tradedproducts in the liquidation set that include the first portfolio productin the first ordering as one of the leg products. In the case of thefirst tree, the first portfolio product in the first ordering is X₁ andthe first level nodes consist of products X₇ (leg products X₁ and X₂)and X₈ (leg products X₁ and X₃). The second level of the first treeincludes all spread-traded products in the liquidation set that includethe second portfolio product in the first ordering as one of the legproducts, but exclude any spread-traded product in the liquidation setthat includes a lower ordered portfolio product as a leg product. In thecase of the first tree, the second portfolio product in the firstordering is X₂ and the second level thus consists of products X₉ (legproducts X₂ and X₃) and X₁₀ (leg products X₂ and X₄). Product X₇ isexcluded from the second level because it includes a lower orderedportfolio product (X₁) as one of its leg products. All of the secondlevel products are added as nodes from each of the first level nodes.The third level of the first tree includes all spread-traded products inthe liquidation set that include the third portfolio product in thefirst ordering as a leg product, but excludes any spread-traded productin the liquidation set that includes a lower ordered portfolio productas a leg product. In the case of the first tree, the third portfolioproduct in the first ordering is X₃ and the third level thus consists ofproducts X₁₁ (leg products X₃ and X₅) and X₁₂ (leg products X₃ and X₆).Products X₈ and X₉ are excluded from the third level because eachincludes a lower ordered portfolio product (X₁ or X₂) as a leg product.All of the third level products are added as nodes from each of thesecond level nodes.

A similar pattern would then be followed for each of the other portfolioproducts based on the position of each remaining product in the firstordering. In the present example, however, this pattern results in noadditional levels for the first tree. The only spread-traded products inthe liquidation set that include the fourth product of the firstordering is product X₁₀. However, that product would be excluded fromthe fourth level because it includes a lower-ordered portfolio product(X₂) as a leg product. A similar result occurs with regard to the fifthand sixth portfolio products (X₅ and X₆) in the first ordering.

After generating all the search trees, module 142 then allocates theportfolio products by progressing through each branch of each tree inboth directions. During a pass (or “traverse”) through a branch, module142 allocates portfolio positions by hypothetically liquidating anentire portfolio position in a product at each level of the tree, evenif that results in a hypothetical increase in a position in anotherproduct. The product for which a position is completely liquidated ateach tree level is the portfolio product associated with that level.

In the example of FIG. 6, and in a downward pass through the firstbranch of the first tree, module 142 determines a first set of interimestimated allocations. At the beginning of this pass, module 142 wouldfirst allocate portfolio positions by completely allocating the positionin the portfolio product associated with level 1 (X₁) to a hypotheticaltrade in the spread-traded product (X₇) at the level 1 node in the firstbranch, resulting in N_(est-int1)(X₇) of 1200. The portfolio only has an$800 million short position in the other X₇ leg product (X₂), however,and the actual portfolio X₂ position would need to be increased by $400million (short) if this X₇ trade were actually carried out. Because theestimated allocation ultimately resulting from step 203 (FIG. 2) will beused as an approximation to narrow a subsequent optimization algorithm,however, this is permitted. Module 142 would then proceed to the secondtree level and completely allocate the position in the portfolio productassociated with level 2 (X₂) to a hypothetical trade in thespread-traded product (X₉) at the level 2 node in the first branch.Because the position in product X₂ has already been liquidated, however,no allocation occurs. Module 142 would then proceed to the third treelevel and completely allocate the position in the portfolio productassociated with level 3 (X₃) to a hypothetical trade in thespread-traded product (X₁₁) at the level 3 node in the first branch,resulting in N_(est-int1)(X₁₁) of 500. The portfolio has a $600 millionshort position in the other X₁₁ leg product (X₅), however, and actuallyexecuting this X₁₁ trade would imply first increasing the initialportfolio X₅ position to $1100 million (short). Again, this would bepermitted. Because the third node is the last in the branch, module 142would allocate the remaining portfolio positions to hypotheticaloutright trades, resulting in a first set of interim estimatedallocations (in millions of $US) of {N_(est-int1)(X₁)=0;N_(est-int1)(X₂)=0; N_(est-int1)(X₃)=0; N_(est-int1)(X₄)=750;N_(est-int1)(X₅)=600; N_(est-int1)(X₆)=1000; N_(est-int1)(X₇)=1200;N_(est-int1)(X₈)=0; N_(est-int1)(X₉)=0; N_(est-int1)(X₁₀)=0;N_(est-int1)(X₁₁)=500; N_(est-int1)(X₁₂)=0}.

Module 142 would then obtain a second set of interim estimatedallocations by performing a similar procedure in a pass in the reversedirection on the first path (X₁₁, X₉, X₇), a third set of interimestimated allocations by performing a similar procedure in a pass downthe second path of the first tree (X₇, X₉, X₁₂), a fourth set of interimestimated allocations by performing a similar procedure in a pass up thesecond path of the first tree (X₁₂, X₉, X₇), etc., until all paths ofall trees have been traversed in both directions. For each set ofinterim estimated allocations, module 142 also calculates a liquidationcost using Equation 3. The set of interim estimated allocationscorresponding to the lowest liquidation cost is then provided, as theresult of step 203 (FIG. 2), to step 204.

FIG. 8 is a flow chart summarizing operations performed by module 142 ofcomputer system 100 in embodiments such as the example described in FIG.7. The steps of FIG. 8 may form step 203 of FIG. 2. In step 351, module142 generates M orderings of the portfolio products into Q rankings,where Q is the number of products represented in the portfolio. Each ofthe M orderings will subsequently be used to generate a search tree. Insome embodiments, the M orderings are all possible orderings. In otherembodiments, and as discussed below, the number of orderings is limited.

In step 352, module 142 initializes the ordering counter m and theranking counter q to 1. In step 353, module 142 begins generating asearch tree for product ordering m. In step 354, module 142 beginsgenerating a level of that search tree associated with the portfolioproduct having ranking q in ordering m. In step 355, module 142identifies all spread-traded products in the liquidation set thatinclude the q-ranked portfolio product as a leg product, but excludesall spread-traded products that include portfolio products have aranking less than q. If there are any resulting spread-traded products,they are then designated as the nodes of the current level of the searchtree. If the current level is the first level, those resulting productsform a single set of nodes. If the current level is after the firstlevel, those resulting products form a separate set of nodes descendingfrom each of the nodes in the previous level. If there are no resultingproducts, no nodes are added.

Module 142 then proceeds to step 356 and determines if q=Q. If not,module 142 increments q by 1 (step 357) and then returns to step 354. Ifq=Q, module 142 proceeds to step 358 and determines if m=M. If not,module 142 proceeds to step 359, stores data indicating the currentsearch tree is complete, and then returns to step 353 to begingenerating the next search tree. If m=M, module 142 proceeds to step360.

In step 360, module 142 selects the search tree paths that will betraversed to generate interim estimated allocations. In someembodiments, module 142 selects each direction through every branch ofevery tree. In other embodiments, and as also discussed below, thenumber of selected paths is more limited. In step 361, module 142identifies one of the paths selected in step 360 as the current path. Instep 362, module 142 identifies the first node of the current path asthe current node. In step 363, module 142 completely allocates anynon-zero position in the portfolio product corresponding to the treelevel of the current node to a hypothetical trade in the spread-tradedproduct corresponding to the current node. In step 364, module 142determines if there are more nodes in the current path. If so, module142 selects the next node in the current path as the current node (step365) then returns to step 363. If not, module 142 proceeds to step 366and determines if there are more selected paths (from step 360) forwhich a set of interim estimated allocations has yet to be determined.If so, module 142 goes to step 367. In step 367, module 142 completesthe current set of interim estimated allocations by allocating anyremaining portfolio positions to hypothetical outright trades in theappropriate portfolio products, saves data corresponding to the currentset of interim estimated allocations, and chooses an untraversed one ofthe selected paths (i.e., a selected path for which a set of interimestimated allocations has not yet been determined) as the current path.From step 367, module 142 then returns to step 362.

If module 142 determines in step 366 that there are no more paths forwhich a set of interim estimated allocations has yet to be determined,module 142 proceeds to step 368. In step 368, module 142 identifies theset of interim estimated allocations corresponding to the lowestestimated liquidation cost. That set of interim estimated allocations isthen selected as the set of estimated allocations N_(est)(X₁) throughN_(est)(X_(k)) and provided to step 204 (FIG. 2).

Generating all possible orderings of portfolio products, and thengenerating interim allocations based on passes (in both directions)through every branch of every tree, could result in extensivecomputations for portfolios with positions in numerous products. Even ifthis is performed, however, there is no assurance that one of theresulting sets of allocations would be optimal. Because the set ofestimated allocations is used as a starting point for furtheroptimization, limiting the number of orderings and/or number of branchesconsidered may be appropriate.

In some embodiments, step 351 includes procedures to limit the number oforderings. As but one example of such procedures, module 142 couldidentify a subset of W products in the portfolio having the largesttotal notional values (where W is a predetermined value, e.g., 5).Module 142 could then generate all possible orderings of those subsetproducts (for a total of W! orderings), and to each of those orderingsappend the remaining portfolio products in the same order. Otherprocedures could be implemented. Similarly, step 360 in some embodimentsmay include procedures to limit the number of branches traversed. As butone example, module 142 might randomly select a predetermined number (orpredetermined percentage up to a maximum number) of the availablebranches.

After obtaining a set of estimated allocations in step 203 (FIG. 2),module 142 performs calculations to determine a set of optimizedallocations in step 204. Like the set of estimated allocations of step203, a set optimized allocations will reflect hypothetical trades inspread-traded and outright-traded products necessary to completelyliquidate the portfolio. As used herein, an “optimized” allocation isnot necessarily the absolute best possible allocation that results inthe lowest possible liquidation cost (although it might be). Instead, anoptimized allocation is one that is calculated using analytical toolsthat are more likely to provide the best possible solution.

As part of optimization step 204, and for a portfolio to which the datain Data Arrays 1 through 3 applies, module 142 creates Equations 4through 5-j.

$\begin{matrix}{{{LC} = {\sum\limits_{i = 1}^{k}{C_{i}\left( {N\left( X_{i} \right)} \right)}}},{{where}\mspace{14mu}{LC}},C_{i},{{and}\mspace{14mu}{N\left( X_{i} \right)}\mspace{14mu}{have}\mspace{14mu}{the}\mspace{14mu}{meanings}\mspace{14mu}{explained}\mspace{14mu}{above}\mspace{14mu}{in}\mspace{14mu}{connection}\mspace{14mu}{with}\mspace{14mu}{Equation}\mspace{14mu} 2.}} & {{Equation}\mspace{14mu} 4} \\{{{{{N_{P}\left( X_{1} \right)} = {{N\left( X_{1} \right)} + {N\left( \left\lbrack {S - {T\text{:}X_{1}}} \right\rbrack_{1} \right)} + \ldots + {N\left( \left\lbrack {S - {T\text{:}X_{1}}} \right\rbrack_{n} \right)}}},{{wherein}\mspace{14mu}{N_{P}\left( X_{1} \right)}\mspace{14mu}{is}\mspace{14mu}{the}\mspace{14mu}{portfolio}\mspace{14mu}{position}\mspace{14mu}{in}\mspace{14mu}{product}\mspace{14mu} X_{1}},{{{and}\mspace{14mu}{{where}\mspace{14mu}\left\lbrack {S - {T\text{:}X_{1}}} \right\rbrack}_{1}\mspace{14mu}{{through}\mspace{14mu}\left\lbrack {S - {T\text{:}X_{1}}} \right\rbrack}_{n}\mspace{14mu}{are}\mspace{14mu}{all}\mspace{14mu}{of}\mspace{14mu}{the}\mspace{14mu}{spread}\text{-}{traded}\mspace{14mu}{products}\mspace{14mu}{from}\mspace{14mu}{the}\mspace{14mu}{liquidation}\mspace{14mu}{set}\mspace{14mu}{that}\mspace{14mu}{include}\mspace{14mu} X_{1}\mspace{14mu}{as}\mspace{14mu} a\mspace{14mu}{leg}\mspace{14mu}{product}};{{``n"}\mspace{14mu}{in}\mspace{14mu}{Equation}\mspace{14mu} 5\text{-}1\mspace{14mu}{will}\mspace{14mu}{not}\mspace{14mu}{necessarily}\mspace{14mu}{have}\mspace{14mu}{the}\mspace{14mu}{same}\mspace{14mu}{values}\mspace{14mu}{as}\mspace{14mu}{``n"}\mspace{14mu}{in}\mspace{14mu}{other}\mspace{14mu}{Equations}\mspace{14mu} 5.}}}\mspace{14mu}\vdots{{{NOTE}\text{:}\mspace{14mu}{there}\mspace{14mu}{will}\mspace{14mu}{be}\mspace{14mu} a\mspace{14mu}{seperate}\mspace{14mu}{Equation}\mspace{14mu} 5},{{similar}\mspace{14mu}{in}\mspace{14mu}{form}\mspace{14mu}{to}\mspace{14mu}{Equations}\mspace{14mu} 5\text{-}1\mspace{14mu}{and}\mspace{14mu} 5\text{-}j},{{for}\mspace{14mu}{each}\mspace{14mu}{of}\mspace{14mu}{portfolio}\mspace{14mu}{products}\mspace{14mu} X_{1}\mspace{14mu}{through}\mspace{14mu}{X_{j}.\mspace{25mu}\vdots}}}}\;} & {{Equation}\mspace{14mu} 5\text{-}1} \\{{{N_{P}\left( X_{j} \right)} = {{N\left( X_{j} \right)} + {N\left( \left\lbrack {S - {T\text{:}X_{j}}} \right\rbrack_{1} \right)} + \ldots + {N\left( \left\lbrack {S - {T\text{:}X_{j}}} \right\rbrack_{n} \right)}}},{{wherein}\mspace{14mu}{N_{P}\left( X_{j} \right)}\mspace{14mu}{is}\mspace{14mu}{the}\mspace{14mu}{portfolio}\mspace{14mu}{position}\mspace{14mu}{in}\mspace{14mu}{product}\mspace{14mu} X_{j}},{{{and}\mspace{14mu}{{where}\mspace{14mu}\left\lbrack {S - {T\text{:}X_{j}}} \right\rbrack}_{1}\mspace{14mu}{{through}\mspace{14mu}\left\lbrack {S - {T\text{:}X_{j}}} \right\rbrack}_{n}\mspace{14mu}{are}\mspace{14mu}{all}\mspace{14mu}{of}\mspace{14mu}{the}\mspace{14mu}{spread}\text{-}{traded}\mspace{14mu}{products}\mspace{14mu}{from}\mspace{14mu}{the}\mspace{14mu}{liquation}\mspace{14mu}{set}\mspace{14mu}{that}\mspace{14mu}{include}\mspace{14mu} X_{j}\mspace{14mu}{as}\mspace{14mu} a\mspace{14mu}{leg}\mspace{14mu}{product}};{{``n"}\mspace{14mu}{in}\mspace{14mu}{Equation}\mspace{14mu} 5\text{-}j\mspace{14mu}{will}\mspace{14mu}{not}\mspace{14mu}{necessarily}\mspace{14mu}{have}\mspace{14mu}{the}\mspace{14mu}{same}\mspace{14mu}{value}\mspace{14mu}{as}\mspace{14mu}{``n"}\mspace{14mu}{in}\mspace{14mu}{other}\mspace{14mu}{Equations}\mspace{14mu} 5.}}} & {{Equation}\mspace{14mu} 5\text{-}j}\end{matrix}$

Equations 5-1 through 5-j describe a constraint to Equation 4.Specifically, Equations 5-1 through 5-j impose a requirement that theportfolio be completely liquidated. Using the example of portfolio P1,module 142 would generate the equations shown in Table 3.

TABLE 3 No. Eq. 4${LC} = {\sum\limits_{i = 1}^{12}\;{C_{i}\left( {N\left( X_{i} \right)} \right)}}$5-1 $1200 M = N(X₁) + N(X₇) + N(X₈) 5-2 $800 M = N(X₂) + N(X₇) + N(X₉) +N(X₁₀) 5-3 $500 M = N(X₃) + N(X₈) + N(X₉) + N(X₁₁) + N(X₁₂) 5-4 $750 M =N(X₄) + N(X₁₀) 5-5 $600 M = N(X₅) + N(X₁₁) 5-6 $1000 M = N(X₆) + N(X₁₂)

After creating Equations 4 through 5-j, module 142 determines values foreach of N(X₁) through N(X_(k)) in Equation 4, while applying theconstraints of Equations 5-1 through 5-j, that result in the lowestvalue LC. Any of numerous known optimization algorithms can be used inconjunction with an optimization based on Equations 4 through 5-j. Suchalgorithms include, without limitation, interior point optimizationalgorithms and active set optimization algorithms. To speed convergenceof the optimization algorithm, the set of estimated allocationsN_(est)(X₁) through N_(est)(X_(k)) from step 203 are used as seed valuesto initialize the optimization algorithm and narrow the range ofpossible allocations to be searched.

In step 205, module 142 determines if a set of allocations having aliquidation cost LC (calculated using Equation 4) less than LC_(est) hasbeen found. The quantity LC_(est) in step 205 represents the liquidationcost associated with the set of estimated allocations N_(est)(X₁)through N_(est)(X_(k)) from step 203 and is calculated from thoseestimated allocations using Equation 3. In some circumstances, forexample, an optimization algorithm may not converge to a solution. Ifmodule 142 determines a set of allocations having a liquidation cost LCless than LC_(est) was not found in step 204, module 142 designatesLC_(est) as LC_(opt) (step 206) and proceeds to step 208. If module 142determines a set of allocations having a liquidation cost LC less thanLC_(est) was found in step 204, module 142 designates that LC asLC_(opt) (step 206) and proceeds to step 208.

In step 208 module 140 determines an amount of a performance bond (or aperformance bond component) based on LC_(opt) and outputs dataindicating that amount. That data may also be transmitted to anappropriate party for use in verifying that the portfolio holder hassufficient funds or other assets on deposit and/or to obtain additionalfunds or assets from the portfolio holder.

Embodiments include additional variations on the procedures outlinedabove. In some embodiments, for example, two techniques are utilized todetermine sets of estimated allocations. The set of estimatedallocations having the lower estimated liquidation cost is then used inan optimization step. FIG. 9 is a flow chart of a method according toone such embodiment. Steps 401, 402, and 406 through 410 arerespectively similar to steps 201, 202, and 204 through 208 of FIG. 2.However, step 203 of the FIG. 2 method has been replaced with steps 403,404 and 405. In step 403, module 142 determines a first set of estimatedallocations N1 _(est)(X₁) through N1 _(est)(X_(k)) using the methoddescribed in connection with FIG. 6. In step 404, module 142 determinesa second set of estimated allocations N2 _(est)(X₁) through N2_(est)(X_(k)) using the method described in connection with FIG. 8. Instep 405, module 142 determines which of the first or second sets ofestimated allocations corresponds to a lower estimated liquidation costand provides that set of estimated allocations as an input to step 406.

In some embodiments, a portfolio may include positions in productshaving notionals defined in different ways. For example, total notionalamounts of positions in a first group of the portfolio products might bequantities of a first currency, total notional amounts of positions in asecond group of the portfolio products might be quantities of a secondcurrency, and total notional amounts of positions in a third group ofthe portfolio products might be quantities of a commodity. The abovedescribed procedures can be adapted to such a portfolio in various ways.As but one example, liquidation cost functions for the second group ofportfolio products and related spread-traded products can be modified(e.g., through use of a current first currency to second currencyexchange rate) to output a cost in terms of the first currency.Similarly, liquidation cost functions for the third group of portfolioproducts and related spread-traded products can be modified (e.g.,through use of a current spot trading rate) to output a cost in terms ofthe first currency.

CONCLUSION

The foregoing description of embodiments has been presented for purposesof illustration and description. The foregoing description is notintended to be exhaustive or to limit embodiments to the precise formexplicitly described or mentioned herein. Modifications and variationsare possible in light of the above teachings or may be acquired frompractice of various embodiments. The embodiments discussed herein werechosen and described in order to explain the principles and the natureof various embodiments and their practical application to enable oneskilled in the art to make and use these and other embodiments withvarious modifications as are suited to the particular use contemplated.Any and all permutations of features from above-described embodimentsare the within the scope of the invention.

The invention claimed is:
 1. A computer implemented method comprising:accessing, by a computer system, a data structure which stores dataindicative of a position in each of a plurality of outright-tradedproducts in a portfolio; identifying, by the computer system, a set ofliquidation products which includes the plurality of outright-tradedproducts and further includes one or more spread-traded products formedby a combination of two or more of the plurality of outright-tradedproducts, wherein each of the liquidation products in the set ofliquidation products is associated with a cost function for estimating aliquidation cost based on notional value of the associated liquidationproduct; using an approximation to limit a number of orderings and anumber of branches considered: determining, by the computer system, aset of estimated allocations of the positions in each of the pluralityof outright-traded products among each of the liquidation products ofthe set of liquidation products; and determining, iteratively by thecomputer system using the set of estimated allocations and theassociated cost functions associated with each liquidation producttherein, the estimated allocation of the set of estimated allocationsthat is characterized by a lowest liquidation cost; and wherein themethod further comprises outputting, by the computer system, dataindicating at least a portion of a performance bond based on thedetermined lowest liquidation cost.
 2. The computer implemented methodof claim 1, wherein the determining of the set of estimated allocationsfurther comprises, for each estimated allocation: ordering the one ormore spread-traded products in the set of liquidation products based onthe cost functions associated therewith; progressing through each of theordered spread-traded products and allocating at least a portion of thepositions in each of the plurality of outright-traded products tohypothetical trades in the spread-traded products; and allocating anyremainder of the positions in each of the plurality of outright-tradedproducts to hypothetical outright trades.
 3. The computer implementedmethod of claim 1, wherein the determining of the set of estimatedallocations further comprises: generating multiple search trees, each ofthe search trees having multiple branches; determining a liquidationcost corresponding to each of at least a portion of the branches in atleast a portion of the search trees; and selecting a set of estimatedallocations corresponding to the branch having a lowest correspondingliquidation cost.
 4. The computer implemented method of claim 1, whereinthe determining of the set of estimated allocations further comprises,for each estimated allocation: determining a first set of estimatedallocations by ordering the spread-traded products in the set ofliquidation products based on the cost functions associated therewith,progressing through each of the ordered spread-traded products andallocating at least a portion of the positions in each of the pluralityof outright-traded products to hypothetical trades in the spread-tradedproducts, and allocating any remainder of the positions in each of theplurality of outright-traded products to hypothetical outright trades;determining a second set of estimated allocations based on one or moresearch trees; determining which of the first set of estimatedallocations and the second set of estimated allocations corresponds to alower liquidation cost; and selecting as the estimated allocations theone of the first set of estimated allocations and the second set ofestimated allocations determined to correspond to a lower liquidationcost.
 5. The computer implemented method of claim 1, wherein thedetermining of the set of estimated allocations further comprisesinputting the estimated allocations as an initial condition for thedetermining of the estimated allocation of the set of estimatedallocations that is characterized by the lowest liquidation cost.
 6. Thecomputer implemented method of claim 5, wherein the determining of theestimated allocation of the set of estimated allocations that ischaracterized by lowest liquidation cost further comprises: computing aliquidation cost for each estimated allocation of the set of estimatedallocations based on the cost function associated with each liquidationproduct therein, and iteratively comparing each computed liquidationcost with a prior computer liquidation to determine the lowestliquidation cost.
 7. The computer implemented method of claim 6, whereinthe computing and comparing are performed until the least liquidationcost of any of the set of estimated allocation is determined.
 8. One ormore non-transitory computer-readable media storing computer executableinstructions that, when executed, cause a computer system to performoperations that include: accessing a data structure which stores dataindicative of a position in each of a plurality of outright-tradedproducts in a portfolio; identifying a set of liquidation products whichincludes the plurality of outright-traded products and further includesone or more spread-traded products formed by a combination of two ormore of the plurality of outright-traded products, wherein each of theliquidation products in the set of liquidation products is associatedwith a cost function for estimating a liquidation cost based on notionalvalue of the associated liquidation product; determining a set ofestimated allocations of the positions in each of the plurality ofoutright-traded products among each of the liquidation products of theset of liquidation products; determining, using the set of estimatedallocations and the associated cost functions associated with eachliquidation product therein, the estimated allocation of the set ofestimated allocations that is characterized by a lowest liquidationcost; and outputting data indicating at least a portion of a performancebond based on the determined lowest liquidation cost.
 9. The one or morenon-transitory computer-readable media of claim 8, wherein thedetermining of the set of estimated allocations further comprises:ordering the spread-traded products in the set of liquidation productsbased on the cost functions associated therewith; progressing througheach of the ordered spread-traded products and allocating at least aportion of the positions in each of the plurality of outright tradedproducts to hypothetical trades in the spread-traded products; andallocating any remainder of the positions in each of the plurality ofoutright traded products to hypothetical outright trades.
 10. The one ormore non-transitory computer-readable media of claim 8, wherein thedetermining of the set of estimated allocations further comprises:generating multiple search trees, each of the search trees havingmultiple branches; determining a liquidation cost corresponding to eachof at least a portion of the branches in at least a portion of thesearch trees; and selecting a set of estimated allocations correspondingto the branch having a lowest corresponding liquidation cost.
 11. Theone or more non-transitory computer-readable media of claim 8, whereinthe determining of the set of estimated allocations further comprises:determining a first set of estimated allocations by ordering thespread-traded products in the set of liquidation products based on thecost functions associated therewith, progressing through each of theordered spread-traded products and allocating at least a portion of thepositions in each of the plurality of outright traded products tohypothetical trades in the spread-traded products, and allocating anyremainder of the positions in each of the plurality of outright tradedproducts to hypothetical outright trades; determining a second set ofestimated allocations based on one or more search trees; determiningwhich of the first set of estimated allocations and the second set ofestimated allocations corresponds to a lower liquidation cost; andselecting as the set of estimated allocation the one of the first set ofestimated allocations and the second set of estimated allocationsdetermined to correspond to a lower liquidation cost.
 12. The one ormore non-transitory computer-readable media of claim 8, wherein thedetermining of the set of estimated allocations further comprisesinputting the set of estimated allocations as an initial condition forthe determining of the estimated allocation of the set of estimatedallocations that is characterized by the lowest liquidation cost. 13.The one or more non-transitory computer-readable media of claim 12,wherein the determining of the estimated allocation of the set ofestimated allocations that is characterized by the lowest liquidationcost further comprises: computing a liquidation cost for each estimatedallocation of the set of estimated allocations based on the costfunction associated with each liquidation product therein, anditeratively comparing each computed liquidation cost with a priorcomputer liquidation to determine the lowest liquidation cost.
 14. Theone or more non-transitory computer-readable media of claim 13, whereinthe computing and comparing are performed until the least liquidationcost of any of the set of estimated allocation is determined.
 15. Acomputer system comprising: at least one processor; and at least onenon-transitory memory, wherein the at least one non-transitory memorystores instructions that, when executed, cause the computer system toperform operations that include: accessing a data structure which storesdata indicative of a position in each of a plurality of outright-tradedproducts in a portfolio; identifying a set of liquidation products whichincludes the plurality of outright-traded products and further includesone or more spread-traded products formed by a combination of two ormore of the plurality of outright-traded products, wherein each of theliquidation products in the set of liquidation products is associatedwith a cost function for estimating a liquidation cost based on notionalvalue of the associated liquidation product; determining a set ofestimated allocations of the positions in each of the plurality ofoutright-traded products among each of the liquidation products of theset of liquidation products; determining, using the set of estimatedallocations and the associated cost functions associated with eachliquidation product therein, the estimated allocation of the set ofestimated allocations that is characterized by a lowest liquidationcost; and outputting data indicating at least a portion of a performancebond based on the determined lowest liquidation cost.
 16. The computersystem of claim 15, wherein the determining of the set of estimatedallocations further comprises: ordering the spread-traded products inthe set of liquidation products based on the cost functions associatedtherewith; progressing through each of the ordered spread-tradedproducts and allocating at least a portion of the positions in each ofthe plurality of outright traded products to hypothetical trades in thespread-traded products; and allocating any remainder of the positions ineach of the plurality of outright traded products to hypotheticaloutright trades.
 17. The computer system of claim 15, wherein thedetermining of the set of estimated allocations further comprises:generating multiple search trees, each of the search trees havingmultiple branches; determining a liquidation cost corresponding to eachof at least a portion of the branches in at least a portion of thesearch trees; and selecting a set of estimated allocations correspondingto the branch having a lowest corresponding liquidation cost.
 18. Thecomputer system of claim 15, wherein the determining of the set ofestimated allocations further comprises: determining a first set ofestimated allocations by ordering the spread-traded products in the setof liquidation products based on the cost functions associatedtherewith, progressing through each of the ordered spread-tradedproducts and allocating at least a portion of the positions in each ofthe plurality of outright traded products to hypothetical trades in thespread-traded products, and allocating any remainder of the positions ineach of the plurality of outright traded products to hypotheticaloutright trades; determining a second set of estimated allocations basedon one or more search trees; determining which of the first set ofestimated allocations and the second set of estimated allocationscorresponds to a lower liquidation cost; and selecting as the set ofestimated allocation the one of the first set of estimated allocationsand the second set of estimated allocations determined to correspond toa lower liquidation cost.
 19. The computer system of claim 15, whereinthe determining of the set of estimated allocations further comprisesinputting the set of estimated allocations as an initial condition forthe determining of the estimated allocation of the set of estimatedallocations that is characterized by the lowest liquidation cost. 20.The computer system of claim 19, wherein the determining of theestimated allocation of the set of estimated allocations that ischaracterized by the lowest liquidation cost further comprises:computing a liquidation cost for each estimated allocation of the set ofestimated allocations based on the cost function associated with eachliquidation product therein, and iteratively comparing each computedliquidation cost with a prior computer liquidation to determine thelowest liquidation cost.